System and method for structured LDPC code family

Abstract

A low density parity check (LDPC) family of codes is constructed by: determining a protograph for a mother code for the LDPC family of codes. The protograph is lifted by a lifting factor to design code specific protograph for a code. The method also includes constructing a base matrix for the code. The base matrix is constructed by replacing each zero in the code specific protograph with a ‘−1’; and replacing each one in the code specific protograph with a corresponding value from the mother matrix. The LDPC code includes a codeword size of at least 1344, a plurality of information bits, and a plurality of parity bits. The LDPC code is based on a mother code of code length 672.

What is claimed is: 
     
       1. A method for constructing a low density parity check (LDPC) family of codes, the method comprising:
 determining, by a Context-based operation Reconfigurable Instruction Set Processor (CRISP), a protograph for a mother code for the LDPC family of codes; 
 lifting the protograph by a lifting factor to design a code specific protograph for a code; and 
 constructing a base matrix for the code, the base matrix constructed by:
 replacing each zero in the code specific protograph with a ‘−1’; and 
 replacing each one in the code specific protograph with a corresponding value from the mother matrix. 
 
 
     
     
       2. The method as set forth in  claim 1 , wherein the mother code comprises a code length of 672. 
     
     
       3. The method as set forth in  claim 1 , further comprising selecting circulant blocks, wherein the selecting comprises:
 lifting the protograph by a lifting factor of one of 2, 3 and 4. 
 
     
     
       4. The method as set forth in  claim 1 , further comprising deriving a second code from the mother code, wherein the second code comprises a second code rate that is lower than the highest code rate. 
     
     
       5. The method as set forth in  claim 4 , wherein the second code comprises at least one of a rate-⅝ code; a rate-½ code and a rate-¾ code. 
     
     
       6. The method as set forth in  claim 4 , wherein the second code comprises a length of at least one of 1344, 2016 and 2688. 
     
     
       7. The method as set forth in  claim 4 , wherein the constructed codes comprise at least one of:
 a same structures as the mother code; 
 a 4-layers decodable; 
 a same row and column degree distribution as the mother code; and 
 can be decoded by a same decoder as the mother code. 
 
     
     
       8. A Context-based operation Reconfigurable Instruction Set Processor (CRISP) decoder configured perform an error correction using a low density parity check (LDPC) code, the LDPC code comprising:
 a codeword size of at least 1344; 
 a plurality of information bits; and 
 a plurality of parity bits, wherein the LDPC code is based on a mother code of code length 672, wherein the LDPC code is constructed by:
 determining a protograph for a mother code for the LDPC family of codes; 
 lifting the protograph by a lifting factor to design a code specific protograph for a code; and 
 constructing a base matrix for the code, the base matrix constructed by:
 replacing each zero in the code specific protograph with a ‘−1’; and 
 replacing each one in the code specific protograph with a corresponding value from the mother matrix. 
 
 
 
     
     
       9. The decoder as set forth in  claim 8 , further comprising at least one of:
 a same structures as the mother code; 
 a 4-layers decodable; 
 a same row and column degree distribution as the mother code; and 
 can be decoded by a same decoder as the mother code. 
 
     
     
       10. The decoder as set forth in  claim 8 , wherein the construction of the LDPC code further comprises:
 selecting circulant blocks, wherein the selecting comprises: 
 lifting the protograph by a lifting factor of one of 2, 3 and 4. 
 
     
     
       11. The decoder as set forth in  claim 8 , further configured to derive a second code from the mother code, wherein the second code comprises a second code rate that is lower than the highest code rate. 
     
     
       12. The decoder as set forth in  claim 11 , wherein the second code comprises at least one of a rate-⅝ code; a rate-½ code and a rate-¾ code. 
     
     
       13. The decoder as set forth in  claim 11 , wherein the second code comprises a length of at least one of 1344, 2016 and 2688. 
     
     
       14. A method comprising:
 performing, by a Context-based operation Reconfigurable Instruction Set Processor (CRISP), an error correction using a low density parity check (LDPC) code from a LDPC family of codes, the LDPC code comprising: 
 a codeword size of at least 1344; 
 a plurality of information bits; and 
 a plurality of parity bits, wherein the LDPC code is based on a mother code, wherein the LDPC code is constructed by:
 determining a protograph for a mother code for the LDPC family of codes; 
 lifting the protograph by a lifting factor to design a code specific protograph for a code; and 
 constructing a base matrix for the code, the base matrix constructed by:
 replacing each zero in the code specific protograph with a ‘−1’; and 
 replacing each one in the code specific protograph with a corresponding value from the mother matrix. 
 
 
 
     
     
       15. The method as set forth in  claim 14 , wherein the mother code comprises a code length of 672. 
     
     
       16. The method as set forth in  claim 14 , further comprising selecting circulant blocks, wherein the selecting comprises:
 lifting the protograph by a lifting factor of one of 2, 3 and 4. 
 
     
     
       17. The method as set forth in  claim 14 , further comprising deriving a second code from the mother code, wherein the second code comprises a second code rate that is lower than the highest code rate. 
     
     
       18. The method as set forth in  claim 17 , wherein the second code comprises at least one of a rate-⅝ code; a rate-½ code and a rate-¾ code. 
     
     
       19. The method as set forth in  claim 17 , wherein the second code comprises a length of at least one of 1344, 2016 and 2688. 
     
     
       20. The method as set forth in  claim 17 , wherein the constructed codes comprise at least one of:
 a same structures as the mother code; 
 a 4-layers decodable; 
 a same row and column degree distribution as the mother code; and 
 can be decoded by a same decoder as the mother code.